Problem solving: Why are students so impatient?

After watching a video about students' abilities to problem solve (Dan Meyer – Math Class Needs a Makeover ), here are a few keys points of interest:

- problems worth solving are not simple.  We often create an environment where students expect to solve problems quickly, making students impatient problem solvers.
- textbooks give students all of the information that they need. Students don't need to filter information or seek out new information - they only need to follow procedures.
- "What matters here?" - a very under-represented question in many math programs. Students are told what matters and do not often need to determine important information for themselves.
- Dan Meyer reduces the information given when introducing a problem to drive conversation, engagement, and perseverance in his students.

Right vs. wrong answers

In Classroom Discussions, the authors write about the importance of mathematical reasoning. It's important for students to have the ability to decide for themselves whether their answers are right or wrong. Instead of telling students whether the answer is or isn't correct, invite others to agree or disagree. Offer multiple answers (generated from your students' work, or even from teacher-created samples) and allow students to explain why they believe one of the answers is the correct one.

Problem-Solving Strategies

The authors of Classroom Discussions talk about how George Polya outlined a four-step problem solving method. It's interesting to me because our school was part of an Action Research project a few years ago that focused on problem-solving. Teachers within our school created a method called "RIDE" (Read It, Imagine and Plan, Do It, Explain). At the time, I didn't realize that it was based off of Polya's method.

The four-step problem-solving method:

1. understand the problem;
2. make a plan for solving the problem;
3. carry out the plan; and
4. look back and reflect on the answer in terms of the initial question.

What to talk about?

Chapter 4 in Classroom Discussions is all about what students should be talking about during Math Congress. Here are some interesting points:

- with young students, partner talk should be framed with a very specific question

- students can talk about how they found their answer, and then compare their strategies with others (e.g., What did you both do that was the same? You both used counting to find the answer? What was different? One of you used manipulatives and the other drew a picture?)

- summarizing what students have been talking about

- instead of having 1 person explain their whole answer, they can talk it through while the teacher records what they say (the student tells the teacher what/where to record their ideas)

- invite students to explain others' answers to encourage student engagement. Check back with the original student. Did they explain your ideas correctly? Do you have anything to add or to explain?

- not everyone understands by hearing the right answers. Choose students with incorrect answers (even after the correct answer has been shared) because students often learn more (and deepen their understanding) when they consider incorrect options and then reject them

 - discuss everything! What does a + mean? Where do we write numbers when recording a multiplication question? Why?

- many students do not understand the meaning of symbols. For example, many students do not see the equal sign (=) as a statement of equivalence or balance. They see it as a signal to "write the answer" (p. 136).

Supporting math talk in the classroom - how can we reinforce and move the talk along?

The authors of Classroom Discussions write about 5 main ways to move the talk along.

1. Revoicing. "So you're saying that it's an odd number..." [This supports students who are not explaining their thinking/ideas in a clear way.]
2. Repeating: Asking students to restate someone else's reasoning. "Can you repeat what he said in your own words?" [Students who repeat ideas will have a better chance of following the conversation. This makes everyone more accountable for the talk time.]
3. Reasoning: Ask students to apply their own reasoning by agreeing or disagreeing. [This builds accountability AND critical thinking, especially when students need to say WHY they agree or disagree.]
4. Adding on: "Would someone like to add something more to this?"
5. Waiting and using wait time. "Take your time... we'll wait..."

 Talk Formats:

a) Whole class discussion
b) Small group discussion
c) Partner talk *

Interesting points:

Often, the teacher refrains from providing the correct answer and instead leads the students towards it with prompts, questioning, rephrasing, and repetition.


* This reminds of me a very interesting teacher that I met during a Ministry of Education conference. She used partners to further talk in her Grade 2 class. She mixed partners up every other week, and students used their "talk buddies" for every kind of Think/Pair/Share for two weeks. She said that it built inclusion and students' willingness to work with everyone. I think that would fit well into this kind of Math program.

How do we make math congress safe?

Establishing a respectful and safe community is important.

1. every student needs to listen to what others say
2. students need to be able to hear what others are saying
3. all students should participate and share ideas at some point

Why is communication during Math important?

After reading only a few chapters in Classroom Discussions, I have already read a number of interesting things. Key points so far:

• Research has been urging teachers to emphasize communication during Math for over 2 decades.
• Learning skills, such as communication, collaboration, and cooperation, fit nicely with this style of teaching.
• Asking different and open ended questions allow students to gain a deeper understanding of concepts.
• Students often understand when teachers explain but do not have a deep enough understanding to put their learning in their own words. "Math talk" does two things: 1. It allows the teacher and student to know how much they really do understand; 2. It forces students to explain what they do understand, thus further deepening their understanding. 

Math congress... how does it work effectively in Grade 1?

There is currently a huge shift in education surrounding inquiry based learning. A major focus of this shift is all about Math. While I have a lot of experience with inquiry based learning through problem solving, I'm excited to make this part of my program even better next year. Last year I really focused on improving my students' abilities to talk about Math and their learning. Questions like, "What were you thinking? Show us with pictures, numbers, and words." and "How would we know what you were thinking if we couldn't ask you?" greatly helped, but I want to take their communication skills even further next year.

I was given the book Classroom Discussions: Using math talk to help students learn, and I'm looking forward to reading it.

My focus question: How do I use math congress effectively in Grade 1?

Why blog?

The reason for starting this blog is simple. I want to record and compile the information, research findings, and ideas that I acquire on my journey as a professional educator. I am hoping that this blog will help me to organize and use everything that I learn easily - and maybe (eventually) it will help someone else too!